期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1989
卷号：12
DOI：10.1155/S0161171289000785
出版社：Hindawi Publishing Corporation
摘要：In this paper, the notion of spatial numerical range of elements of Banach
algebras without identity is studied. Specifically, the relationship between spatial
numerical ranges, numerical ranges and spectra is investigated. Among other results,
it is shown that the closure of the spatial numerical range of an element of a Banach
algebra without Identity but wlth regular norm is exactly its numerical range as an
element of the unitized algebra. Futhermore, the closure of the spatial numerical
range of a hermitian element coincides with the convex hull of its spectrum. In
particular, spatial numerical ranges of the elements of the Banach algebra C0(X)
are
described.
